Kerry Back
BUSI 721, Fall 2022
JGSB, Rice University
At times, the market is turbulent, and at times it is quite calm.
Daily returns are drawn from a mixture of distributions:
high std dev in turbulent times and low std dev in calm times.
Most outliers occurred in turbulent times
- when std dev was high
Normal distribution with 0 mean and std dev sometimes =1=1 and sometimes =4=4
kde plot of the mixture and a plot of the normal pdf with the same mean and std dev
Compute std dev (volatility) of return in each calendar month
import numpy as np
import pandas as pd
from scipy.stats import norm
import matplotlib.pyplot as plt
x1 = pd.Series(norm.rvs(0,1,1000))
x2 = pd.Series(norm.rvs(0,4,1000))
x = pd.concat((x1, x2))
mn = x.mean()
sd = x.std()
grid = np.linspace(mn-3*sd, mn+3*sd, 101)
y = norm.pdf(grid, mn, sd)
_ = x.plot(kind="kde", label="mixture")
_ = plt.plot(grid, y, label="normal")
_ = plt.legend()